In Greg's hat, he has $1$ yellow, $2$ red, and $3$ green tokens. One red token is equivalent to $7$ yellow tokens. One yellow token is equivalent to $3$ green tokens. Greg converts all of his tokens to green tokens. How many green tokens does he have?
Answer: We are given the conversion factors $$\frac{7\text{ yellow tokens}}{1\text{ red token}} = 1  \text{and}  \frac{3\text{ green tokens}}{1\text{ yellow token}} = 1.$$We first convert all of Greg's red tokens to yellow tokens: $$2\text{ red tokens}\cdot \frac{7\text{ yellow tokens}}{1\text{ red token}} = 14\text{ yellow tokens}.$$Greg now has a total of $15$ yellow tokens, which we now convert to green tokens: $$15\text{ yellow tokens}\cdot \frac{3\text{ green tokens}}{1\text{ yellow token}} = 45\text{ green tokens}.$$ Adding these $45$ green tokens to the $3$ that Greg already had, we see that Greg has $\boxed{48}$ green tokens.